#### How do I calculate the Equation of Time?

The Equation of Time is the difference: apparent solar time minus mean solar time.

##### Windows edition

To compute the Equation of Time, select Positions from the Calculate menu. Next, select the Sun and the Apparent Geocentric Equator of Date position type. Specify the UT1 time scale in the Date/Time/Location dialog box. Select the starting date of interest and set the repetitions, as appropriate. The equation of time is tabulated in the far right column of the output table (see sample below). "Calculating Apparent Geocentric Position of Sun (equator of date) and Equation of Time" in the MICA 2.2.2 Help also describes this procedure.

##### Macintosh edition

To compute the Equation of Time, select Positions of the Sun from the Compute menu. In the Coordinates view of the Positions dialog box, select the Geocentric Origin, Apparent Place, Date Reference Epoch, Equator Reference Plane, and Spherical Coordinates parameters. In the Date/Time view of the same dialog box, specify the UT1 time scale. Select the starting date of interest. Set the repetitions, as appropriate, using the Repetitions view. The equation of time is tabulated in the far right column of the output table (see sample below). "Equation of Time" in the MICA 2.2.2 Help also describes this procedure.

```                                    Sun

Apparent Geocentric Positions
True Equator and Equinox of Date

Date        Time          Right       Declination     Distance     Equation
(UT1)              Ascension                                   of Time
h  m   s     h  m   s         °  '   "         AU          m   s
2011 Dec 22 05:30:00.0   17 59 59.993   - 23 26 12.45   0.983750298   + 1 44.1
2011 Dec 23 05:30:00.0   18 04 26.499   - 23 25 58.13   0.983690804   + 1 14.2
2011 Dec 24 05:30:00.0   18 08 53.017   - 23 25 15.55   0.983634852   + 0 44.2
2011 Dec 25 05:30:00.0   18 13 19.503   - 23 24 04.74   0.983582397   + 0 14.3
2011 Dec 26 05:30:00.0   18 17 45.917   - 23 22 25.73   0.983533484   - 0 15.5
```

Because the Equation of Time does not apply to atomic time, it will not be displayed if the TT time scale is selected.

```                                    Sun

Apparent Geocentric Positions
True Equator and Equinox of Date

Date        Time      Right Ascension     Declination        Distance
(TT)
h  m   s       h  m   s           °  '   "          AU
2011 Dec 22 05:30:00.0     17 59 59.787     - 23 26 12.45    0.983750345
2011 Dec 23 05:30:00.0     18 04 26.294     - 23 25 58.15    0.983690848
2011 Dec 24 05:30:00.0     18 08 52.811     - 23 25 15.60    0.983634894
2011 Dec 25 05:30:00.0     18 13 19.298     - 23 24 04.81    0.983582436
2011 Dec 26 05:30:00.0     18 17 45.712     - 23 22 25.82    0.983533520
```

#### Why do the times of sunrise/sunset not appear to change with height above the earth?

MICA assumes a level horizon in its calculation of rise/set times. Therefore, the dip of the horizon is not taken into consideration when calculating these times. However, the refraction of the light does change, because the light at altitude is not passing through as much atmosphere as it does at sea level. In most circumstances, these changes are small, usually less than a minute in rise/set time. Because the rise/set times are printed only to the nearest minute, you usually will not see any differences. However, at high latitudes, the times can change by several minutes (see the example for Barrow, Alaska below).

```                                      Sun

Location:  W156°47'19.0", N71°17'26.0",     0m
(Longitude referred to Ephemeris meridian)

Date         Begin      Rise  Az.   Transit Alt.    Set  Az.     End
(TT)         Astron.                                            Astron.
Twilight                                           Twilight
h  m     h  m   °      h  m  °       h  m   °      h  m
2005 Jan 21 (Fri)   16:47    ----- ---     ----- ---     ----- ---     04:28
2005 Jan 22 (Sat)   16:45    22:20 176     22:39  0S     22:59 185     04:31
2005 Jan 23 (Sun)   16:42    21:57 170     22:39  0S     23:22 190     04:34
2005 Jan 24 (Mon)   16:40    21:43 167     22:39  0S     23:37 194     04:37
2005 Jan 25 (Tue)   16:37    21:31 164     22:40  1S     23:49 197     04:41

Sun

Location:  W156°47'19.0", N71°17'26.0", 10999m
(Longitude referred to Ephemeris meridian)

Date         Begin      Rise  Az.   Transit Alt.    Set  Az.     End
(TT)         Astron.                                            Astron.
Twilight                                           Twilight
h  m     h  m   °      h  m  °       h  m   °      h  m
2005 Jan 21 (Fri)   16:47    ----- ---     ----- ---     ----- ---     04:28
2005 Jan 22 (Sat)   16:45    22:13 174     22:39  0S     23:06 186     04:31
2005 Jan 23 (Sun)   16:42    21:53 169     22:39  0S     23:26 191     04:34
2005 Jan 24 (Mon)   16:40    21:40 166     22:39  0S     23:40 194     04:37
2005 Jan 25 (Tue)   16:37    21:29 163     22:40  1S     23:52 197     04:41
```

#### Although I chose decimal format in the Preferences Dialog box (Windows)/on the Settings menu (Mac), why is the sidereal time output still in HMS (hours/minutes/seconds)?

The global preferences for output format apply to Positions, Configurations, and Galilean Moons calculations. At this time, MICA does not allow customization of the Date & Time calculations, including sidereal time.

#### Although I chose decimal format in the Preferences Dialog box (Windows)/on the Settings menu (Mac), why is the Earth Rotation Angle (ERA) output still in DMS (degrees/minutes/seconds)?

The global preferences for output format apply to Positions, Configurations, and Galilean Moons calculations. At this time, MICA does not allow customization of the Date & Time calculations, including Earth Rotation Angles.

#### What should I do in response to the "C:\Users\Administrator\AppData\Roaming\U.S.NavalObservatory\MICA\custom.ump is corrupt. Custom location coordinates will not be available." message that appears when I start MICA on my Windows computer?

Assuming you are "Administrator," the custom locations binary file (custom.ump) for this specific user is corrupt. This directory is normally hidden, so you must "Show hidden files, folders, or drives" in Windows Explorer to access the file. Restore custom.ump from a previously working backup or delete it and a new, empty one will be created at MICA startup.

If MICA was installed for all users, each local user will have his/her own individual custom.ump file in his/her own Users\ <username>\AppData\Roaming\U.S. Naval Observatory\MICA directory. By Windows default, individual users have "write" permission to their corresponding AppData directory.

#### What should I do in response to the "Delta T file not found" alert that appeared after I updated to/installed MICA 2.2.x on my PowerPC Macintosh computer?

Due to an error during file creation, the MICA Delta T file for PowerPC (PPC) Macs has incorrect file permissions. PPC Macs will not be able to access the file, and the "Delta T file not found" alert will appear when MICA starts. A package that will install the corrected Delta T file is available on the Willmann-Bell Web site.

Intel-based Macs are not affected by this problem.

#### Does MICA 2 have a batch mode like the MICA 1.x PC version did?

MICA 2 does not have a batch mode capability. One of our developers spent quite a bit of time trying to develop a batch mode for the Windows operating system, but was unsuccessful. The Windows operating system is quite different from the old DOS-based operating system on which MICA 1.x was based, and the old method would not work under the Windows operating system.

#### Why do the magnitudes of Mercury and Venus computed by MICA occasionally differ from those printed in The Astronomical Almanac?

Several people have noted that the magnitudes of Mercury and Venus as given by MICA 2 can differ slightly compared to those in The Astronomical Almanac (AsA). Until the 2005 edition of the AsA, both MICA and the AsA used the same algorithms based on Harris (1961). However, the 2005 and 2006 editions of the AsA adopted formulations for the magnitudes based on Hilton (2003), prior to that material being published in the refereed literature. During the refereeing process, new observational data became available and the formulas were revised. These new formulas, based on Hilton (2005), were used in the AsA starting with the 2007 edition. Meanwhile, MICA 2.0 continued to use the Harris formulas because those of Hilton had not been published while MICA 2.0 was in development. Beginning with MICA 2.1, MICA adopted the Hilton (2005) formulas.

##### In summary:

The AsA 2004 and earlier editions, MICA 2.0 and MICA 1.5 should give the same answer and are based on the following references:

• Harris, D. L., 1961, in Planets and Satellites edited by G. P. Kuiper and B.A. Middlehurst (Chicago: Univ. Chicago Press), pp. 272–342.
• Values for V(1,0), the visual magnitude at unit distance, are given on page E88 of the 2004 edition of the AsA.

The AsA 2005 and 2006 editions are based on:

MICA 2.1 and 2.2 and the AsA 2007 and later editions are based on:

##### Recommendation:

For years 2007 and later, use MICA 2.2 and/or the AsA values. For years 2006 and earlier, use MICA 2.2.